#6 For a bcc cube, assume it is fully packed (atoms touch one another):

2. A pn junction diode has the doping profile sketched in the figure below. Make the assumption that Xn>xo for all applied biases of interest (Xn follows the same definition as in the lecture). (a) What is the built-in voltage across the junction? Justify your answer. (b) Invoking the depletion approximation, sketch the charge density p versus x inside the diode. (c) Obtain an analytical solution for the electric field, E(x), inside the depletion region. ND-NA Not N₂2 Xo -NA

1. Draw the circuit schematic for the voltage doubler, like Figure 4. Use an input signal of 1 kHz sine wave with an amplitude of 0.7 Vrms. Assume the forward threshold voltage of the diode is 0.4 V. Use Rs = 100 , RL = 10 kn. Assume CB is fully charged at steady state. 2. Calculate the peak output voltage at steady state. [A-2] 3. Calculate the expected peak-to-peak ripple voltage due to capacitor C₁ discharging. [A-3] 4. Calculate the DC value, which is given by the average value of the ripple wave. [X-1] To find this, you will have to find how much the output voltage discharges through RL. Then find the time-average of the steady-state DC signal during the charging and discharging cycles. 5. Record the values in Table 1. [T-1] 6. Sketch the input and output waveforms in steady state, showing two waves, clearly labeling all axes and marking all relevant voltage and time values. [A-4] [A-1]

4. Concentration questions with a twists a) A silicon wafer is uniformly doped p-type with NA=1016/cm³. At T = OK, what are the equilibrium hole and electron concentrations? b) A semiconductor is doped with an impurity concentration N such that N >> n; and all the impurities are ionized. Also, p = N and n = n²/N. Is the impurity a donor or an acceptor? Explain. c) The electron concentration in a piece of Si maintained at 300K under equilibrium conditions is 10%/cm³. What is the hole concentration? d) For a silicon sample maintained at T = 300K, the Fermi level is located 0.518eV above the intrinsic Fermi level. What are the hole and electron concentrations? e) In a nondegenerate germanium sample maintained under equilibrium conditions near room temperature, it is known that n₁ = 10¹³/cm³, n = 3p, and N₁ = 0. Determine n and ND.

Part a: The number of transistors per IC in 1972 seems to be about 4,000 (a rough estimate by eye). Using this estimate and Moore's Law, what would you predict the number of transistors per IC to be 20 years later, in 1992? Prediction = ?

1. A Si step junction maintained at room temperature under equilibrium conditions has a p- side doping of N₁=3 x 10¹5/cm³ and an n-side doping of ND=2 x 10¹5/cm³. Compute (a) Vbi (b) Xp, Xn and W (c) E at x = 0 (d) V at x = 0 (e) Make sketches that are roughly to scale of the charge density, electric field, and electrostatic potential as a function of position.

Say, you want to make a digital logic circuit made of fast n type and p type devices. You have materials A,B,C,D to choose from. The ratio of electron effective masses for materials A,B,C and D is 1:2:4:3. The ratio of hole effective masses for materials A,B,C and D are 4:1:3:2. Which materials from A,B,C and D you would like to choose for making those fast n type and p type devices?

2. A Si crystal that is 2cm³ in size has been n-type doped uniformly at a ratio of 1 in 105. The intrinsic concentration of silicon is 1 x 10¹0 cm³ and its atomic concentration is 5 x 1022 cm³. Figure 1 shows how the drift mobility varies with dopant concentration at room temperature (300K). a) What is the donor concentration? b) What is the hole concentration? c) Using the graph in Figure 1 and your answers to a) and b), calculate the electrical resistance of the n-type doped silicon crystal. d) We now dope the silicon crystal with boron atoms instead of arsenic to create a p-type semiconductor. We again doped the crystal uniformly at a ratio of 1 in 10 What is the electrical resistance now? Compare your result to that obtained in c), giving a reason for any difference.

#5 For a Si bar of length 5 cm, doped n-type at 10¹5 cm3, calculate the current density for an applied voltage of 2.5V across its length. (10 points) The electron mobility = 1500

#4 In terms of the lattice constant a, show the formula to calculate the distance between nearest- neighbor atoms for: A: a bcc lattice? (10 points) B: a fcc lattice? (10 points)

Assignment #1 #8 identify two crystalline directions, or vectors, in a cubic crystal which are perpendicular to the [100] vector (5 points) Note: the cosine of the angle between three arbitrary vectors [h1, k1,11], [h2,k2,12] and [h3,k3,13] in 3D is: cos(0) = Fall 2023 h₁h₂+k₁k₂ + ₁42 (h₁² + k₁² + 1₁₂²) (h₂² + k₂² +1₂²)